Bayesiananalysisof stellarparameters inPTPS

Michalina Górecka1, Beata Deka1, Andrzej Niedzielski11Torun Centre for Astronomy, Nicolaus Copernicus University, ul. Gagarina 11, 87-100 Torun, Poland

IntroductionMass is the most important parameter which determines internal structure and evolution of a star. In case of planet searches with the precise radialvelocity measurements technique the stellar mass is required to estimate the minimum mass of a planetary companion. Precise mass determinationsfor stars are not simple, though. Best stellar mass measurements come from the Third Kepler Law which describes motion of two orbiting bodies.In the case of eclipsing binaries masses can be measured with an accuracy that depends on the quality of observational data only. Indirect stellarmass estimates usually use other characteristics adequate to the evolutionary stage i.e.: for the main sequence star the Eddington mass-luminosityrelation (Eddington 1924), for white dwarfs the mass-radius relation (Panei et al. 2000). Another approach to obtain stellar mass is to compare stellarevolutionary models (Bertelli 2008; Bressan 2012) with available observational data delivered (detailed spectroscopically determined atmosphericparameters, photometry and parallaxes) for instance by isochrone fitting or bayesian probability approach.The sample of stars comes from ongoing PennState-Torun Centre for Astronomy Planet Search (PTPS, Niedzielski & Wolszan 2008) focused ondetecting and characterazing planetary systems around stars at various evolutionary stages. It contains 332 relatively bright, field stars, mostlygiant with G8-K2 spectral type. Atmospheric parameters required to mass, age and luminosity estimation was determined by Zielinski et al. (2012).Astrophysical parameters estimated by χ2 fitting of stellar atmospheric parameters are also presented there.

Bayesian probability approachWe implemented method based on Jor-gensen & Lindegren (2005) formalism andmodified by da Silva et. al. (2006) toavoid statistical biases and to take errorestimates of observed quantities into con-sideration. For given star, representedby full set of available atmospheric pa-rameters: [Fe/H]∗ ± σ[Fe/H]∗ , log Teff∗ ±σlog Teff∗ , log g∗±σlog g∗ and logL∗±σlogL∗

(if parallax available) and isochrone of[Fe/H] and age t we calculated in therange [M1

i ,M2i ] the probability:

P12 ∝∫M2

i

M1iφ(Mi)dMi · exp

(−χ2

)with

χ2 = (log g−log g∗)2

σ2log g∗

+(log Teff−log Teff∗)

2

σ2log Teff∗

and φ(m) ∝ m−2.35 is the Initial MassFunction (Salpeter 1955). We further fol-low the procedure detailed in da Silva et.al. (2006) and calculate searched

quantities (e.g. mass, luminosity and age)and their uncertainties from basic param-eters (mean, variance) of the normalizedPDFs. In comparison with other parame-ters the widest distribution and the low-est probability peak is present in the caseof log(age/yr). As a consequence stellarages obtained here are most uncertain.

Example of PDF for TYC 1211 15.

HRD for 332 PTPS stars

Stellar parameters

Because of well estimated logarithm of surface gravitywe implemented this parameter instead of absolute mag-nitude like da Silva et al. (2006).

Comparison with Zielinski et al. 2012

Stellar masses obtained here, with average value of 1.3M� are generally lower (0.88)than those of Zielinski et al. (2012) - 1.5 M� but the abundant population of stars withmasses is now absent. The resulting stellar masses are also more precise.

Acknowledgements

AN was supported by the Polish Ministry of NCN grant N N203 510938. AN, BD, MG are currently supported by NCN grant2012/07/B/ST9/04415. The HET is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University,Ludwig-Maximilians-Universität München, and Georg-August-Universität Göttingen. The HET is named in honor of its principal benefactors,William P. Hobby and Robert E. Eberly. The Center for Exoplanets and Habitable Worlds is supported by the Pennsylvania State University and theEberly College of Science.